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        <h2>
          <span class="refentrytitle">phaser1</span>
        </h2>
        <p>phaser1 — 
      First-order allpass filters arranged in a series.
          </p>
      </div>
      <div class="refsect1">
        <a id="idp133808016"></a>
        <h2>Description</h2>
        <p>
      An implementation of <span class="emphasis"><em>iord</em></span> number of first-order allpass filters in series.
   </p>
      </div>
      <div class="refsect1">
        <a id="idp133849696"></a>
        <h2>Syntax</h2>
        <pre class="synopsis">ares <span class="command"><strong>phaser1</strong></span> asig, kfreq, kord, kfeedback [, iskip]</pre>
      </div>
      <div class="refsect1">
        <a id="idp133851952"></a>
        <h2>Initialization</h2>
        <p>
      <span class="emphasis"><em>iskip</em></span> (optional, default=0) -- used to control initial disposition of internal data space. Since filtering incorporates a feedback loop of previous output, the initial status of the storage space used is significant. A zero value will clear the space; a non-zero value will allow previous information to remain. The default value is 0.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133854272"></a>
        <h2>Performance</h2>
        <p>
      <span class="emphasis"><em>kfreq</em></span> -- frequency (in Hz) of the filter(s). This is the frequency at which each filter in the series shifts its input by 90 degrees. 
    </p>
        <p>
      <span class="emphasis"><em>kord</em></span> -- the number of allpass stages in series. These are first-order filters and can range from 1 to 4999.
    </p>
        <div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
          <table border="0" summary="Note: Note">
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              </td>
              <th align="left">Note</th>
            </tr>
            <tr>
              <td align="left" valign="top">
                <p>
        Although <span class="emphasis"><em>kord</em></span> is listed as k-rate, it is in fact accessed only at init-time. So if you are using a k-rate argument, it must be assigned with <a class="link" href="init.html" title="init"><em class="citetitle">init</em></a>.
      </p>
              </td>
            </tr>
          </table>
        </div>
        <p>
      <span class="emphasis"><em>kfeedback</em></span> -- amount of the output which is fed back into the input of the allpass chain. With larger amounts of feedback, more prominent notches appear in the spectrum of the output. <span class="emphasis"><em>kfeedback</em></span> must be between -1 and +1. for stability.
    </p>
        <p>
      <span class="emphasis"><em>phaser1</em></span> implements <span class="emphasis"><em>iord</em></span> number of first-order allpass sections, serially connected, all sharing the same coefficient. Each allpass section can be represented by the following difference equation:
      </p>
        <div class="literallayout">
          <p><br />
y(n) = C * x(n) + x(n-1) - C * y(n-1)<br />
      </p>
        </div>
        <p>
      where x(n) is the input, x(n-1) is the previous input, y(n) is the output, y(n-1) is the previous output, and C is a coefficient which is calculated from the value of <span class="emphasis"><em>kfreq</em></span>, using the bilinear z-transform.
    </p>
        <p>
      By slowly varying <span class="emphasis"><em>kfreq</em></span>, and mixing the output of the allpass chain with the input, the classic "phase shifter" effect is created, with notches moving up and down in frequency. This works best with <span class="emphasis"><em>iord</em></span> between 4 and 16. When the input to the allpass chain is mixed with the output, 1 notch is generated for every 2 allpass stages, so that with <span class="emphasis"><em>iord</em></span> = 6, there will be 3 notches in the output. With higher values for <span class="emphasis"><em>iord</em></span>, modulating <span class="emphasis"><em>kfreq</em></span> will result in a form of nonlinear pitch modulation.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133868336"></a>
        <h2>Examples</h2>
        <p>
      Here is an example of the phaser1 opcode. It uses the file <a class="ulink" href="examples/phaser1.csd" target="_top"><em class="citetitle">phaser1.csd</em></a>.

      </p>
        <div class="example">
          <a id="idp133870192"></a>
          <p class="title">
            <strong>Example 620. Example of the phaser1 opcode.</strong>
          </p>
          <div class="example-contents">
            <p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
            <pre class="programlisting">
<span class="csdtag">&lt;CsoundSynthesizer&gt;</span>
<span class="csdtag">&lt;CsOptions&gt;</span>
<span class="comment">; Select audio/midi flags here according to platform</span>
<span class="comment">; Audio out   Audio in    No messages</span>
-odac           -iadc     -d     <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o phaser1.wav -W ;;; for file output any platform</span>
<span class="csdtag">&lt;/CsOptions&gt;</span>
<span class="csdtag">&lt;CsInstruments&gt;</span>

<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 1

<span class="comment">; demonstration of phase shifting abilities of phaser1.</span>
<span class="oblock">instr</span> 1
  <span class="comment">; Input mixed with output of phaser1 to generate notches.</span>
  <span class="comment">; Shows the effects of different iorder values on the sound</span>
  idur   <span class="op">=</span> p3 
  iamp   <span class="op">=</span> p4 <span class="op">*</span> .05
  iorder <span class="op">=</span> p5        <span class="comment">; number of 1st-order stages in phaser1 network.</span>
                     <span class="comment">; Divide iorder by 2 to get the number of notches.</span>
  ifreq  <span class="op">=</span> p6        <span class="comment">; frequency of modulation of phaser1</span>
  ifeed  <span class="op">=</span> p7        <span class="comment">; amount of feedback for phaser1</span>

  kamp   <span class="opc">linseg</span> 0, .2, iamp, idur <span class="op">-</span> .2, iamp, .2, 0

  iharms <span class="op">=</span> (<span class="ohdr">sr</span><span class="op">*</span>.4) <span class="op">/</span> 100

  asig   <span class="opc">gbuzz</span> 1, 100, iharms, 1, .95, 2  <span class="comment">; "Sawtooth" waveform modulation oscillator for phaser1 ugen.</span>
  kfreq  <span class="opc">oscili</span> 5500, ifreq, 1
  kmod   <span class="op">=</span> kfreq <span class="op">+</span> 5600

  aphs   <span class="opc">phaser1</span> asig, kmod, iorder, ifeed

  <span class="opc">out</span>    (asig <span class="op">+</span> aphs) <span class="op">*</span> iamp
<span class="oblock">endin</span>


<span class="csdtag">&lt;/CsInstruments&gt;</span>
<span class="csdtag">&lt;CsScore&gt;</span>

<span class="comment">; inverted half-sine, used for modulating phaser1 frequency</span>
<span class="stamnt">f</span>1 0  16384 9 .5 -1 0
<span class="comment">; cosine wave for gbuzz</span>
<span class="stamnt">f</span>2 0  8192 9 1 1 .25

<span class="comment">; phaser1</span>
<span class="stamnt">i</span>1 0  5 7000 4  .2 .9
<span class="stamnt">i</span>1 6  5 7000 6  .2 .9
<span class="stamnt">i</span>1 12 5 7000 8  .2 .9
<span class="stamnt">i</span>1 18 5 7000 16 .2 .9
<span class="stamnt">i</span>1 24 5 7000 32 .2 .9
<span class="stamnt">i</span>1 30 5 7000 64 .2 .9
<span class="stamnt">e</span>


<span class="csdtag">&lt;/CsScore&gt;</span>
<span class="csdtag">&lt;/CsoundSynthesizer&gt;</span>
</pre>
          </div>
        </div>
        <p><br class="example-break" />
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133874512"></a>
        <h2>Technical History</h2>
        <p>
      A general description of the differences between flanging and phasing can be found in Hartmann [1]. An early implementation of first-order allpass filters connected in series can be found in Beigel [2], where the bilinear z-transform is used for determining the phase shift frequency of each stage. Cronin [3] presents a similar implementation for a four-stage phase shifting network. Chamberlin [4] and Smith [5] both discuss using second-order allpass sections for greater control over notch depth, width, and frequency.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133876784"></a>
        <h2>References</h2>
        <p>
      </p>
        <div class="orderedlist">
          <ol class="orderedlist" type="1">
            <li class="listitem">
              <p>
            Hartmann, W.M. "Flanging and Phasers." Journal of the Audio Engineering Society, Vol. 26, No. 6, pp. 439-443, June 1978. 
          </p>
            </li>
            <li class="listitem">
              <p>
            Beigel, Michael I. "A Digital 'Phase Shifter' for Musical Applications, Using the Bell Labs (Alles-Fischer) Digital Filter Module." Journal of the Audio Engineering Society, Vol. 27, No. 9, pp. 673-676,September 1979. 
          </p>
            </li>
            <li class="listitem">
              <p>
            Cronin, Dennis. "Examining Audio DSP Algorithms." Dr. Dobb's Journal, July 1994, p. 78-83.
          </p>
            </li>
            <li class="listitem">
              <p>
            Chamberlin, Hal. Musical Applications of Microprocessors. Second edition. Indianapolis, Indiana: Hayden Books, 1985.
          </p>
            </li>
            <li class="listitem">
              <p>
            Smith, Julius O. "An Allpass Approach to Digital Phasing and Flanging." Proceedings of the 1984 ICMC, p. 103-108.
          </p>
            </li>
          </ol>
        </div>
        <p>
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133884256"></a>
        <h2>See Also</h2>
        <p>
      <a class="link" href="phaser2.html" title="phaser2"><em class="citetitle">phaser2</em></a>
          </p>
        <p> Other information about phasers on Wikipedia: <a class="ulink" href="http://en.wikipedia.org/wiki/Phaser_(effect)" target="_top"><em class="citetitle">http://en.wikipedia.org/wiki/Phaser_(effect)</em></a></p>
        <p>
    </p>
      </div>
      <div class="refsect1">
        <a id="idp133887600"></a>
        <h2>Credits</h2>
        <p>
      </p>
        <table border="0" summary="Simple list" class="simplelist">
          <tr>
            <td>Author: Sean Costello</td>
          </tr>
          <tr>
            <td>Seattle, Washington</td>
          </tr>
          <tr>
            <td>1999</td>
          </tr>
        </table>
        <p>
    </p>
        <p>November 2002. Added a note about the <span class="emphasis"><em>kord</em></span> parameter, thanks to Rasmus Ekman.</p>
        <p>New in Csound version 4.0</p>
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